# Chapter 3 - Worked Solutions

### to selected Complex Reasoning questions from the OUP text *Senior
Physics - Knowledge, Processes and Reasoning* by Walding,
Rapkins and Rossiter

**Question 30**

(a)

(b)

(c)

BC = 8 sin 18°
= 2.5 ms^{-1}

BD = 5.0 ms^{-1} in direction W18°
S

** Question 31**

(a) F_{H} = 100 sin 60°
= 87 N

(b) F_{V} = 100 cos 60°
= 50N

** Question 32**

v_{PG} = 250/0.5 = 500 km^{-1} E

v_{AG} = 50 kmh^{-1} N (not S); hence v_{GA} = 50 kmh^{-1} S

v_{PA} = v_{PG} + v_{GA} = 500 kmh^{-1} E + 50 kmh^{-1} S

v_{PA } = 502.5 kmh^{-1} ; angle q
= tan^{-1} 50/500 = 5.7°
; hence direction is E 5.7°
S

** Question 33**

d_{P} = 4 d_{Q }and r_{P} = 4 r_{Q}

(a) A_{P} = 4p
r_{P}^{2}

A_{Q} = 4p
(r_{P}/4)^{2} = 4p
r_{P}^{2} /16 = A_{Q}/16

Hence A_{P} = A_{Q}/16

(b) V_{P} = 4/3 p
r_{P}^{3}

V_{Q} = 4/3 p
r_{Q} (1/4)^{3}

Hence V_{P} = V_{Q}/64

(c) m_{P} = r
V_{P}

m_{Q} = r
V_{Q}

m_{P }= m_{Q}/64

(d) r
_{P} = r
_{Q}

**Question 34**

(a) V_{1} = 35 V_{2}

4/3 p
r_{1}^{3} = 35 x 4/3 p
r_{2}^{2}

(b)

**Question 37 (New Century edition)**

Square both sides of the equation to give: Z^{2} = R^{2} + 4p
^{2}L^{2}f^{2
}

Rearrange the equation to: Z^{2} = 4p
^{2}L^{2}f^{2} + R^{2
}

This is now in the form y = mx + c

where the slope (m) = 4p
^{2}L^{2} and the intercept on the y-axis (c) = R^{2}.

Plot the graph:

Slope = (44100 - 10000)/90000 = 0.379

4p
^{2}L^{2} = 0.379

L = 0.098 metres

Intercept = 10000 = R^{2
}

Therefore R = 100 ohm

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